메뉴 건너뛰기




Volumn 27, Issue 4, 1972, Pages 21-69

Gibbs measures in ergodic theory

(1)  Sinai, G Ya a  

a NONE

Author keywords

[No Author keywords available]

Indexed keywords


EID: 84956071330     PISSN: 00360279     EISSN: None     Source Type: Journal    
DOI: 10.1070/RM1972v027n04ABEH001383     Document Type: Article
Times cited : (882)

References (56)
  • 2
    • 0002564801 scopus 로고
    • Geodesic flows on closed Riemannian manifolds of negative curvature
    • D. V. Anosov, Geodesic flows on closed Riemannian manifolds of negative curvature, Trudy Mat. Inst. Steklov 90 (1967). MR 36 #7157
    • (1967) Trudy Mat. Inst. Steklov , vol.90 , pp. 7157
    • Anosov, D.V.1
  • 4
    • 84956198331 scopus 로고
    • On tangential fields
    • D. V. Anosov, On tangential fields of transversal fiberings in Y-systems, Mat. Zametki 2(1967), 539-548. MR 39 #3523
    • (1967) Mat. Zametki , vol.2
    • Anosov, D.V.1
  • 6
    • 0002336855 scopus 로고
    • Some smooth ergodic systems
    • D. V. Anosov and Ya. G. Sinai, Some smooth ergodic systems, Uspekhi Mat. Nauk 22:5(1967), 107-172. MR 37 #370
    • (1967) Uspekhi Mat. Nauk , vol.22 , Issue.5
    • Anosov, D.V.1    Sinai, G.Y.2
  • 8
    • 84855267255 scopus 로고
    • On some mathematical problems of
    • N. N. Bogolyubov and B. I. Khatset, On some mathematical problems of the theory of statistical equilibrium, Dokl. Akad. Nauk 66 (1949), 321-324. MR 11-40
    • (1949) Dokl. Akad. Nauk , vol.66 , pp. 321-324
    • Bogolyubov, N.N.1    Khatset, B.I.2
  • 9
    • 23944497387 scopus 로고
    • A mathematical description of the equilibrium state of classical systems on the basis of a formalism of a canonical ensemble
    • N. N. Bogolyubov, O. Ya. Petrina, and B. I. Khatset, A mathematical description of the equilibrium state of classical systems on the basis of a formalism of a canonical ensemble, Teoret. Mat. Fiz. 1 (1969), 251-274
    • (1969) Teoret. Mat. Fiz , vol.1 , pp. 251-274
    • Bogolyubov, N.N.1    Petrina, O.Y.2    Khatset, B.I.3
  • 10
    • 84956137282 scopus 로고
    • Small random perturbations of dynamical systems
    • A. D. Ventsel' and M. I. Freidlin, Small random perturbations of dynamical systems, Uspekhi Mat. Nauk 25:1 (1970), 3-55. MR 42 #2123
    • (1970) Uspekhi Mat. Nauk , vol.25 , Issue.1
    • Ventsel, A.D.1    Freidlin, M.I.2
  • 14
    • 84931387388 scopus 로고
    • Some conditions for the existence of A-partitions for
    • B. M. Gurevich, Some conditions for the existence of A-partitions for special flows, Trudy Moskov. Mat. Obshch., 17 (1967), 89-116. MR 37 #5362
    • (1967) Trudy Moskov. Mat. Obshch. , vol.17
    • Gurevich, B.M.1
  • 16
    • 84936832928 scopus 로고
    • On an invariant measure with maximal entropy for a Y-diffeomorphism
    • B. M. Gurevich, On an invariant measure with maximal entropy for a Y-diffeomorphism, Funktsional. Anal. i Prilozhen. 4 (1970), 21-30
    • (1970) Funktsional. Anal. I Prilozhen. , vol.4 , pp. 21-30
    • Gurevich, B.M.1
  • 17
    • 0000482894 scopus 로고
    • Topological Entropy of a countable Markov chain
    • B. M. Gurevich, Topological entropy of a countable Markov chain, Dokl. Akad. Nauk 187 (1969), 715-718. MR 41 #7767
    • (1969) Dokl. Akad. Nauk , pp. 7
    • Gurevich, B.M.1
  • 19
    • 2342623690 scopus 로고
    • Algebraic automorphisms of the torus and Markov chains
    • Appendix to the Russian translation of: P. Billingsley
    • B. M. Gurevich and Ya. G. Sinai, Algebraic automorphisms of the torus and Markov chains, Appendix to the Russian translation of: P. Billingsley, Ergodic theory and information, Wiley, New York 1965. MR 41 # 1969
    • (1965) Ergodic Theory and Information
    • Gurevich, B.M.1    Sinai, G.Y.2
  • 21
    • 0038563682 scopus 로고
    • The connection between different entropy characteristics of dynamical systems
    • E. I. Dinaburg, The connection between different entropy characteristics of dynamical systems, Izv. Akad. Nauk 35 (1971), 324-366
    • (1971) Izv. Akad. Nauk , vol.35 , pp. 324-366
    • Dinaburg, E.I.1
  • 22
    • 0038020323 scopus 로고
    • Gibbs random fields for lattice systems with pairwise interactions
    • R. L. Dobrushin, Gibbs random fields for lattice systems with pairwise interactions, Funktsional. Anal, i Prilozhen. 2 (1968), 31-43. MR 40 # 3867
    • (1968) Funktsional. Anal, I Prilozhen , vol.2
    • Dobrushin, R.L.1
  • 24
    • 33748250931 scopus 로고
    • Zur Umkehrbarheit der statistischen Naturgesetze
    • A. Kolmogoroff, Zur Umkehrbarheit der statistischen Naturgesetze, Math. Ann. 113 (1937), 766-772
    • (1937) Math. Ann , vol.113 , pp. 766-772
    • Kolmogoroff, A.1
  • 25
    • 84956198336 scopus 로고
    • On invariant measures compatible with smoothness for transitive Y-systems
    • A. N. Livshitz and Ya. G. Sinai, On invariant measures compatible with smoothness for transitive Y-systems, Dokl. Akad. Nauk (1973)
    • (1973) Dokl. Akad. Nauk
    • Livshitz, A.N.1    Sinai, G.Y.2
  • 26
    • 84956198337 scopus 로고
    • On certain measures associated with Y-flows
    • G. A. Margulis, On certain measures associated with Y-flows, Funktsional. Anal. i Prilozhen 4 (1970), 62-76. MR 42 #7865
    • (1970) Funktsional. Anal.
    • Margulis, G.A.1
  • 28
    • 0040612396 scopus 로고
    • Some applications of ergodic theory to the investigation of manifolds of negative curvature
    • G. A. Margulis, Some applications of ergodic theory to the investigation of manifolds of negative curvature, Funktsional. Anal. i Prilozhen. 3 (1969), 89-90. MR 41 #2582
    • (1969) Funktsional. Anal. I Prilozhen , vol.3 , pp. 89-90
    • Margulis, G.A.1
  • 30
    • 84956109441 scopus 로고
    • The Gibbs limit distribution, Funktsional
    • R. A. Minlos, The Gibbs limit distribution, Funktsional. Anal. i Prilozhen. 1 (1967), 40-54
    • (1967) Anal. I Prilozhen. , vol.1 , pp. 40-54
    • Minlos, R.A.1
  • 31
    • 0000033355 scopus 로고
    • Convergence of random processes and limit theorems in probability theory
    • Yu. V. Prokhorov, Convergence of random processes and limit theorems in probability theory, Teor. Veroyatnost. i Primenen. 1 (1956), 177-238. MR 18-943
    • (1956) Teor. Veroyatnost. I Primenen , vol.1
    • Prokhorov, V.Y.1
  • 32
    • 84956198338 scopus 로고
    • Selected problems of the metrical theory of dynamical systems
    • V. A. Rokhlin, Selected problems of the metrical theory of dynamical systems, Uspekhi Mat. Nauk 4:2 (1949), 57-128. MR 11-40
    • (1949) Uspekhi
    • Rokhlin, V.A.1
  • 33
    • 0003108925 scopus 로고
    • Lectures on entropy theory of transformations with an invariant measure
    • V. A. Rokhlin, Lectures on entropy theory of transformations with an invariant measure, Uspekhi Mat. Nauk 22:5 (1967), 3-56. MR 37 #349
    • (1967) Uspekhi Mat. Nauk , Issue.5 , pp. 3-56
    • Rokhlin, V.A.1
  • 37
    • 0002486181 scopus 로고
    • Classical Dynamical Systems With Countably-Multiple Lebesgue Spectrum
    • Ya. G. Sinai, Classical dynamical systems with countably-multiple Lebesgue spectrum, II, Izv. Akad. Nauk SSSR Ser. Mat. 30 (1966), 15-68. MR 33 # 5847
    • (1966) Izv. Akad. Nauk SSSR Ser. Mat.
    • Sinai, G.Y.1
  • 38
    • 0002131294 scopus 로고
    • Markov partitions and Y-diffeomorphisms
    • Ya. G. Sinai, Markov partitions and Y-diffeomorphisms, Funktsional. Anal. i Prilozhen 2(1968), 64-89. MR 38 # 1361
    • (1968) Funktsional. Anal. , vol.2 , pp. 64-89
    • Sinai, G.Y.1
  • 39
    • 0001418208 scopus 로고
    • The construction of Markov partitions
    • Ya. G. Sinai, The construction of Markov partitions, Funktsional. Anal. i Prilozhen 2 (1968), 70-80. MR 40 #3591
    • (1968) Funktsional. Anal.
    • Sinai, G.Y.1
  • 41
    • 84931759277 scopus 로고
    • Mesures invariantes des Y-systemes
    • Ya. G. Sinai, Mesures invariantes des Y-systemes, Actes Congrès Internat. des Math. 2, Nice 1970, 929-940
    • (1970) Actes Congrès Internat. Des Math , vol.2 , pp. 929-940
    • Sinai, G.Y.1
  • 42
    • 84956198342 scopus 로고
    • R. Z. Khas’minskii, On the principle of averaging for parabolic and elliptic differential equations and Markov processes with small diffusion, Teor. Veroyatnosti i Primenen. 8 (1963), 3-25. MR 28 #4253
    • (1963) Teor. Veroyatnosti , vol.8
    • Khas’minskii, R.Z.1
  • 43
    • 84931789232 scopus 로고
    • On the number of invariant measures with maximal entropy for displacement in the space of sequences
    • M. S. Shtil’man, On the number of invariant measures with maximal entropy for displacement in the space of sequences, Mat. Zametki 9 (1971), 291-302
    • (1971) Mat. Zametki , vol.9 , pp. 291-302
    • Shtil’man, M.S.1
  • 45
    • 84956072250 scopus 로고
    • A complete metric invariant
    • R. L. Adler, and B. Weiss, Entropy, a complete metric invariant for automorphisms of the torus, Proc. Nat. Acad. Sci. USA 57 (1967), 1250-1252
    • (1967) Proc. Nat. Acad. Sci , vol.57 , pp. 1250-1252
    • Adler, R.L.1    Entropy, B.W.2
  • 46
    • 84956198343 scopus 로고
    • Problèmes ergodiques de la mécanique classique
    • V. I. Arnold and A. Avez, Problèmes ergodiques de la mécanique classique, Gauthiers- Villars, Paris 1967
    • (1967) Gauthiers- Villars
    • Arnold, V.I.1    Avez, A.2
  • 47
    • 0001968927 scopus 로고
    • Markov
    • R. Bowen, Markov partitions and minimal sets for Axiom A diffeomorphisms, Amer.J. Math. 92(1970), 907-918
    • (1970) J. Math , vol.92 , pp. 907-918
    • Bowen, R.1
  • 48
    • 84968508586 scopus 로고
    • Non-commuting random products
    • H. Furstenberg, Non-commuting random products, Trans. Amer. Math. Soc. 108 (1963), 377-408
    • (1963) Trans. Amer. Math. Soc , vol.108 , pp. 377-408
    • Furstenberg, H.1
  • 49
    • 0346365272 scopus 로고
    • R. Gangolli, On the construction of certain diffusions on a differentiable manifold, Z. Wahrscheinlichkeitstheorie u. Verw. Gebiete 2 (1964), 406-419
    • (1964) , vol.2 , pp. 406
    • Gangolli, R.1
  • 50
    • 84867562332 scopus 로고
    • K. Itô, On stochastic differential equations in a differentiable manifold, Nagoya Math. J. 1 (1950), 35-47
    • (1950) Nagoya Math. , pp. 35-47
    • Itô, K.1
  • 51
    • 0000799233 scopus 로고
    • Observables at infinity and states with short-range correlations in statistical mechanics
    • O. Lanford and D. Ruelle, Observables at infinity and states with short-range correlations in statistical mechanics, Comment. Math. Phys. 3 (1968), 194-215
    • (1968) Comment. Math. Phys , vol.3 , pp. 194-215
    • Lanford, O.1    Ruelle, D.2
  • 52
    • 0002815390 scopus 로고
    • A one-to-one representation of geodesics on a surface of negative curvature
    • M. Morse, A one-to-one representation of geodesics on a surface of negative curvature, Amer. J. Math. 43 (1921), 33-51
    • (1921) Amer. J. Math , vol.43 , pp. 33-51
    • Morse, M.1
  • 53
    • 84968480689 scopus 로고
    • Intrinsic Markov chains
    • W. Parry, Intrinsic Markov chains, Trans. Amer. Math. Soc. 114 (1965), 55-66
    • (1965) Trans.Amer.Math.Soc , vol.114 , pp. 55-66
    • Parry, W.1
  • 54
    • 0000333996 scopus 로고
    • D. Ruelle, Statistical mechanics of a one-dimensional lattice gas, Comment. Math. Phys. 9 (1968), 267-278
    • (1968) Comment. Math. Phys , vol.9
    • Ruelle, D.1
  • 55
    • 84956198346 scopus 로고
    • Vere-Jones, Ergodic properties of non-negative matrices, I, II, Pacific J. Math.22(1967), 361-386;
    • (1967) , pp. 361-386
    • Jones, V.1
  • 56
    • 84972574281 scopus 로고
    • Vere-Jones, Ergodic properties of non-negative matrices, I, II, Pacific J. Math.26 (1968). 601-620
    • (1968) , vol.26
    • Jones, V.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.